During a news conference following small- and large-group meetings the two attended this morning, Panetta said he informed the general today that “the United States Navy will invite China to send a ship to participate in the RIMPAC [Rim of the Pacific] 2014 exercise.”

The biannual exercise, hosted by the commander of the U.S. Pacific Fleet, is the world’s largest maritime exercise. It involved 22 nations’ navies this year.

The secretary said he hopes China’s participation in RIMPAC 2014 will build on the positive momentum generated by a counterpiracy exercise the two nations took part in last week in the Gulf of Aden.

“These exercises enhance the ability of our navies to work together to confront the common threat of piracy,” Panetta said.

The secretary said he and Liang also discussed establishing peacekeeping exchanges between the two militaries, which “would enhance our capabilities in this critical area.”

The United States hopes in particular, he added, that through such exchanges “we can learn from China’s experience leading [United Nations] peacekeeping missions in Cyprus and in the Western Sahara”

As the two nations increase cooperation, the secretary said, it’s important for both sides to recognize they won’t always agree.

“The United States continues to be concerned about challenges to maritime security in East Asia,” Panetta said, referring to recent clashes between China and Japan over the Senkaku Islands, known in China as the Diaoyu Islands. In that and other territorial disputes in the Asia-Pacific region, Panetta said, he urges calm and hopes to see the nations involved keep communication channels open so they can resolve their claims peacefully, though diplomacy.

“It’s in no country’s interest for this situation to escalate into conflict that would undermine peace and stability in this very important region,” he added. “This has been my consistent message throughout the week.”

The secretary is midway through an Asia trip that began in Japan and will end later this week with a stop in New Zealand.

Panetta said in discussion with Liang, he also repeated the U.S. desire to have a military-to-military dialogue with China on conduct in cyberspace, which the secretary called a growing economic and security threat.

Finally, Panetta said, he focused during today’s discussions on the U.S. strategic rebalance to the Asia-Pacific region. The United States intends its strategy to add impetus to economic, diplomatic and security interests in the region, which is vital to world trade, the secretary added.

“As I pointed out, a key to that rebalancing is having a constructive relationship with China,” he said.

Liang told reporters during the conference the Chinese government has placed “great value” on Panetta’s visit.

The general confirmed the events on the secretary’s schedule through today: meetings here with Chinese Vice President Xi Jinping, State Councilor Dai Bingguo, who serves in a position roughly equivalent to the U.S. national security advisor; and Vice Chairman of the Central Military Commission Xu Caihou.

Liang also confirmed Panetta’s schedule includes visits to the People’s Liberation Army armored engineering college, where the secretary will deliver a speech, and a visit to the eastern port city of Qingdao, where he will meet with the commander of China’s North Sea Fleet.

The general said that in today’s meetings, “we have exchanged ideas and opinions on bilateral and military-to-military relations between our two nations, on international and regional situations, and … other issues of common interest. We have reached some consensus.”

Liang said both sides agreed “solid and steady development of China-U.S. relations is significant to the two countries, the two peoples, and to the entire world.”

Liang said he and Panetta agreed that within the larger picture of relations between the two countries, they must develop a new military-to-military relationship “based on equality, mutual benefit and win-win cooperation.”

He noted there are issues -- including U.S. arms sales to Taiwan, the U.S. rebalancing strategy in the Asia-Pacific region, territorial disputes in the South and East China Sea, cybersecurity and outer space – on which better communication could “reduce suspicions and build trust.”

The general added that discussions with Panetta have been conducted in a “candid, practical and constructive atmosphere.”